# Calculus

posted by .

1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2].
2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[-4,-2]. If Rolle's Theorem can be applied, find all values of c in the open interval (-4,-2) such that f'(c)=0.
3. Determine whether the open intervals on which the graph of f(x)=-7x+7cosx is concave upward or downward.
4. Find the points of inflection and discuss the concavity of the function f(x)=sinx-cosx on the interval (0,2pi)
5.Find the points of inflection and discuss the concavity of the function f(x)=-x^3+x^2-6x-5

• Calculus -

1.
f' = -pi sin(pi*x) extrema where f' = 0, or x an integer

2.
since f(x) = (x+4)(x+2) f(-4)=f(-2)=0, so we're good to do. vertex is at x = -3.

3.
f is concave up if f'' > 0
f'' = -7cosx, so where is that >0? <0?

4.
concavity as above, inflection where f'' = 0
f'' = -sinx + cosx = √2 sin(x + π/4)

5.
same methods as in #3,4/
f'' = -6x

## Similar Questions

1. ### calc

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. f(x)= x sqrt(x+21) , [-21,0] If there is more than one solution …
2. ### calc

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers "c" that satisfy the conclusion of Rolle's Theorem. f(x)=sin4pix , [-1/2,1/2] Well according to Rolle's Theorem, …

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers "c" that satisfy the conclusion of Rolle's Theorem. f(x)=sin4pix , [-1/2,1/2] Well according to Rolle's Theorem, …
4. ### calculus

Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the three hypotheses of Rolle’s theorem on the interval [0,3]. Then find the values of c on the interval [0,3] that are guaranteed by Rolle’s theorem. Give your answer …
5. ### Math

Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. (Select all that apply.) f (x) = sin(x), [0, 2π] If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that …
6. ### Calculus

1. Determine whether Rolle's Theorem applied to the function f(x)=((x-6)(x+4))/(x+7)^2 on the closed interval[-4,6]. If Rolle's Theorem can be applied, find all numbers of c in the open interval (-4,6) such that f'(c)=0. 2. Determine …
7. ### calculus

determine whether the mean value theorem can be applied to f on the closed interval [a,b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a,b) such that f(c) =f(b) - f(a) / b - a
8. ### Calculus

Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(x)=0. f(x) = x^(2/3) - 1 [-8,8] I plugged in both values …
9. ### calculus

Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = x^2/3 − 2, [−8, 8] 1) Yes, Rolle's Theorem can be applied. 2)No, because f is not continuous on the closed …
10. ### calculus

Rolle's theorem cannot be applied to the function f(x) = x1/3 on the interval [–1, 1] because Answer Choices: f is not differentiable on the interval [–1, 1] f(–1) ≠ f(1) f is not differentiable on the interval [–1, 1] and …

More Similar Questions